have been investigated in the past in some specific cases ([1]}, [2]}, [3]}, [4]}, [5]}, [6]}).
Recently, Pletser showed ([7]}) that, first, for square integer
values of \(k\) , there are either no or only one solution of (REF ),
depending on the value of \(k\) ; and second, for non-square integer
values of \(k\) , there are infinitely many solutions of (REF )
and recurrent relations can be found for the four variables \(t,\xi ,Tt\) 
and \(T_{\xi }\)
\(t_{n} & =2\left(\kappa +1\right)t_{n-r}-t_{n-2r}+\kappa \\\xi _{n} & =2\left(\kappa +1\right)\xi _{n-r}-\xi _{n-2r}+\kappa \\T_{t_{n}} & =\left(4\left(\kappa +1\right)^{2}-2\right)T_{t_{n-r}}-T_{t_{n-2r}}+\left(T_{\kappa }-\gamma \right)\\T_{\xi _{n}} & =\left(4\left(\kappa +1\right)^{2}-2\right)T_{\xi _{n-r}}-T_{\xi _{n-2r}}+k\left(T_{\kappa }-\gamma \right)\) 
